Bachelor’s thesis: Results on cloaking by transformation optics and anomalous localized resonance in elliptic geometry
Published:
In October 2021, I graduated in Physics from the Università degli Studi di Milano. My thesis was conducted under the supervision of Professor Giulio Ciraolo, a member of the math department.
The study of cloaking, that is the ability of hiding obejcts from electromagnetic waves, is an interesting and overgrowning field of physics, engineering and mathematics. Two options are available.
- The first one is transformation optics. By exploiting the invariance of elliptic PDEs under diffeomorphisms and the non-uniqueness of the conductivity from boundary data (Dirichlet–Neumann map, as in EIT), it is possible design cloaking devices.
- The second one is cloaking by anomalous localized resonance (CALR). In this case, the energy of the system localizes and blows up in a shell while fields cancel outside a compact set, making sources undetectable.
The project aimed to extend some results on transformation optics and CALR, namely this one and this one, which provide theoretical results on cloaking and explicit estimates in circular geometry systems. More precisely, the goal was both to provide a theoretical introduction to cloaking and to present explicit results in elliptical geometry, where methods for representing solutions are still available.